A rotorcraft, and in particular a helicopter, is fitted with at least one engine to provide it with lift and propulsion. The engine is fastened to the structure of said rotorcraft and produces driving torque used for rotating the main rotor. The reaction to a single main rotor generates torque in yaw tending to cause the fuselage to turn in the opposite direction to the direction of rotation of the main rotor. In order to compensate this torque, manufacturers generally install a tail or “anti-torque” rotor at the rear of a rotorcraft fuselage, which rotor has blades that are nearly always of variable pitch and under the control of the pilot using the pedals.
Naturally, such an anti-torque rotor also contributes to performing yaw maneuvers and to steering the rotorcraft.
The Fenestron® anti-torque device comprises a ducted rotor or propeller of diameter that is smaller than the diameter of a conventional tail rotor, in particular because of the need to incorporate it in the tail structure of the rotorcraft. Ducting covers the propeller and channels the aerodynamic flow. The rotor housed in this way within a duct has a larger number of blades than that of a conventional tail rotor because of the small diameter of the propeller. For example, the Fenestron® of the Gazelle® helicopter (total weight 2000 kilograms (kg)) designed by the Applicant has 13 blades, whereas the conventional tail rotor of the Super Puma® helicopter, also from the same Applicant, has only four blades even though the rotorcraft has a total weight of about 9000 kg.
Whether conventional or ducted, a tail rotor is a source of noise of aerodynamic origin, as are the engines. The other noises have mechanical sources: engine gearboxes, main transmission box and auxiliary equipment, tail transmission, structural vibration.
In general, the noise problem has two distinct aspects:                noise external to the rotorcraft; and        internal noise, i.e. noise within a cabin of the rotorcraft.        
Under such conditions, the invention applies more particularly to a method of minimizing the external noise generated by a ducted tail rotor anti-torque device, and consequently the invention also relates to a ducted tail rotor anti-torque device obtained by said method. As a natural consequence, internal noise is also reduced.
From the point of view of external noise, it is fundamental that the noise produced at short distances from the takeoff and landing zone does not lead to excessive annoyance.
Furthermore, the use of a rotorcraft in a built-up area also implies flying over an inhabited area and consequently to generating sound nuisance for the population.
Similarly, using a rotorcraft for military purposes also requires consideration to be given to sound emission, since noise enables a rotorcraft to be detected prematurely and to be identified.
Furthermore, it is specified by way of information that the design and disposition of a ducted tail rotor anti-torque device, its rotary drive means, and its means for collective control of the pitch of its blades, and also the advantages of this configuration, are all described in numerous patents in the name of the Applicant, amongst which particular mention can be made of French patents FR 1 531 536 and FR 2 534 222 that describe rotors with blades that are uniformly distributed angularly and that correspond respectively to means for changing the pitch simultaneously of all of the blades, and to various features concerning in particular the blades, and also to an arrangement whereby a rotor and a “deflector” stator are combined for the purpose of recovering the rotary energy from the airflow downstream from the rotor, and using it in the form of axial thrust.
It is also important to mention French patents FR 2 719 549, FR 2 719 550, and FR 2 719 551 in the name of the Applicant and relating to a ducted tail rotor anti-torque device comprising a rotor with a deflector stator, the blades of the ducted rotor then not being uniformly distributed angularly. More precisely, said blades have an angular distribution with an irregular azimuth modulation determined by a sinusoidal relationship so as to contribute to diminishing the noise caused by air flowing through the duct.
That said, it is established that the noise from a rotor comes both from stable and from fluctuating aerodynamic loads acting on the blades. When analyzed using narrow band noise analysis, that noise appears in the form of multiple distinct frequencies, with multiple tones at the frequency at which the blades go past a reference point, referred to more simply as the “blade frequency”.
In other words, the product of a speed of rotation Ω expressed in hertz (Hz), i.e. in revolutions per second, multiplied by a given number b of blades (where b is greater than the number to be found on a conventional tail rotor) gives a blade frequency (bΩ) and multiples thereof (“x”: multiplication sign), in the following form F:                for a rotor with uniform distributed blades:F=n×b×Ωwhere n equals a positive integer;        for a rotor having non-uniformly distributed blades:F=[(n×b)±m]×Ωwhere n, m are positive integers.        
These frequencies in which acoustic energy is concentrated are much higher than the frequencies that occur with a conventional tail rotor, and these frequencies typically lie in the range 400 Hz to 2000 Hz, with the fundamental frequency generally being situated in the range 400 Hz to 600 Hz, and with harmonics of significant level up to very high numbers, the acoustic levels of these harmonics increasing in principle with the “helical” Mach number at the ends of the blades (combination of the circumferential speed at the tips of the blades and the axial speed of the airflow, i.e. substantially normal to the plane of rotation of said blades).
The above frequencies that apply to any ducted anti-torque rotor are attenuated very quickly in the atmosphere. Nevertheless, the fact of raising the frequencies at which acoustic energy is concentrated places said frequencies in a frequency zone where the human ear has maximum sensitivity. Furthermore, the highly impulsive appearance of the noise spectrum of a ducted anti-torque rotor, where most of the acoustic energy is concentrated on two or three very narrow primary spectrum lines, gives rise to a whistling sound that is painful for the human ear, and that is penalized by the criteria for acoustic certification that make use of “emerging spectrum line or pure tone correction”.
The above-mentioned solution consisting in placing the blades so that they are not uniformly distributed performs acoustic interferometry, thereby avoiding concentrating all of the acoustic energy essentially on the fundamental frequency (highest acoustic level), or on a few harmonics, but instead spreading said acoustic energy over intermediate frequencies (between 0 and bΩ, bΩ and 2bΩ, . . . for example), better tolerated by the human ear, which cannot distinguish between two pure tones when they are separated by less than one-third of an octave, thereby attenuating the whistling sound.